Phase-based optical interferometric techniques are widely employed in optical distance measurements in which sub-wavelength distance sensitivity is required. Optical distance is defined as the product of the refractive index and the length. However, most such techniques are limited by an issue which is widely known in the field as 2π ambiguity or integer ambiguity which can be defined as the difficulty in telling the interference fringes of an axial scan apart from each other. An unmodified harmonic phase based low coherence interferometry method (HPI) can be used to determine the differential optical distance, (nλ2−nλ1)L, where L is the physical distance, nλ1 and nλ2 are the refractive indices at the wavelengths λ1 and λ2 respectively, if the optical distance is increased gradually so that the differential phase measured by HPI can be tracked through its 2π wrap over. To determine (nλ2−nλ1) for DNA in solution, for example, the DNA concentration is gradually increased in the measuring cuvette. While such a measurement approach works well in a controlled environment, it can hardly be implemented in a situation where there is less manipulability in the sample. For example, the method does not work on a fixed slab of material which we are constrained to keep whole.
The problem lies in the fact that unmodified HPI is unable to tell the interference fringes of an axial scan apart from each other, described herein as the 2π ambiguity issue. It is a problem that plagues most phase-based optical interferometric techniques. As a result, these techniques are unable to determine optical distance absolutely. Therefore, most such techniques are used in applications, such as evaluating the texture of continuous surfaces or detecting time-dependent distance changes, in which phase unwrapping is possible through comparison of phases between adjacent points or over small time increments.